Question

diffrential calculus find nth derivative the following X/1+3x+2x^2​

Answer 1

Answer:

Step-by-step explanation:

x/(2x^2+3x+1)

First, we factorize the (2x^2+3x+1)

x/(2x+1)(x+1)

Now we do Partial Fraction.

x/(2x+1)(x+1)=A/(x+1)-B/(2x+1)------------(i)

multiple both side by (2x+1)(x+1)

we get,

x=A(2x+1)-B(x+1)

Now,we subsitude with x=-1

so we get B=2 and A=1

so now put the value of A and B in  (i)

we  get

  =1/(x+1)-2/(2x+1)

now add corollary (-1)^(n-1)*n!*a^n/(ax+b)^n

so we get

(-1)^n*n!(1/(x+1)^(n+1)-2^n/(2x+1)^n+1)